The following graph shows a proportional relationship.

Mathematics

1 answer:

MAXImum [283]2 years ago

6 0

The constant of proportionality of the given graph is gotten as 4.

<h3>How to find the constant of proportionality?</h3>

The constant of proportionality here is simply the slope of the graph.

Now, we will take two points and use their coordinates to find the slope from the formula;

m = (y2 - y1)/(x2 - x1)

Let us pick 2 points which are;

(1, 4) and (2, 8). Thus;

m = (8 - 4)/(2 - 1)

m = 4/1

m = 4

Thus, the constant of proportionality of the graph is gotten as 4.

Read more about constant of proportionality at; brainly.com/question/1835116

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Can anyone explain those marked steps in case (iii)

Tema [17]

$\cos\dfrac{3x}2=\cos\left(\dfrac\pi2+\dfrac x2\right)$
$\implies \dfrac{3x}2=2n\pi+\dfrac\pi2+\dfrac x2$

follows from the fact that the cosine function is $2\pi$ -periodic, which means $\cos x=\cos(2\pi+x)$ . Roughly speaking, this is the same as saying that a point on a circle is the same as the point you get by completing a full revolution around the circle (i.e. add $2\pi$ to the original point's angle with respect to the horizontal axis).

If you make another complete revolution (so we're effectively adding $4\pi$ ) we get the same result: $\cos x=\cos(4\pi+x)$ . This is true for any number of complete revolutions, so that this pattern holds for any even multiple of $\pi$ added to the argument. Therefore $\cos x=\cos(2n\pi+x)$ for any integer $n$ .

Next, because $\cos(-x)=\cos x$ , it follows that $\cos x=\cos(2n\pi-x)$ is also true for any integer $n$ . So we have

$\implies \dfrac{3x}2=2n\pi\pm\left(\dfrac\pi2+\dfrac x2\right)$

The rest follows from considering either case and solving for $x$ .